# How to add distortion numbers

Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.

#### jan.didden

Paid Member
How do I 'vector add' or subtract distortion figures?

For example: I have a generator that shows -110dB THD. Sending it through a circuit gives -105dB. What's the distortion of the circuit? What's the general equation for this sort of thing?

Jan

RMS?

#### jan.didden

Paid Member

Yes but how? Do I convert the dB numbers back to voltage ratio, RMS sum the voltage ratios and then convert to dB? Seems a bit awkward, must be a simpler way.

Jan

#### esgigt

Do I convert the dB numbers back to voltage ratio, RMS sum the voltage ratios and then convert to dB?

Jan
Seems to me the way to go, Jan...

Cheers,
Edwin

#### cliffforrest

Agreed, seems simplest - to a non math expert.

A spreadsheet will minimise the burden.

#### anatech

Paid Member
Hi Jan,
It would seem to me that you can't add these numbers directly. The resulting number we get from the meter is like a DC value on a meter, but it is derived from a chaotic waveform composed of noise from every connection that exists while you are measuring. I think you would have to add the squares and take the root in order to get a good guesstimate.

Nothing in electronics is that easy as a scalar addition of two entirely different wave forms unless the delta T approaches 0.
-Chris

#### jan.didden

Paid Member
Hi Jan,
It would seem to me that you can't add these numbers directly. The resulting number we get from the meter is like a DC value on a meter, but it is derived from a chaotic waveform composed of noise from every connection that exists while you are measuring. I think you would have to add the squares and take the root in order to get a good guesstimate.

Nothing in electronics is that easy as a scalar addition of two entirely different wave forms unless the delta T approaches 0.
-Chris

Chris, point taken. I think for worst-case I should assume that there is no (partial) cancellation. But surely many of the heavy lifters here have been confronted with the issue and I would really hate to re-invent the wheel, again!

Jan

#### jan.didden

Paid Member
If I treat the numbers as dBV, convert to Vrms, compute the difference and then back to dB I get -106.5dB with a generator that has -110dBV and a result of -105dBV. Not sure that's correct though.

Jan

#### anatech

Paid Member
Hi Jan,
That's the point. Measurement uncertainty.
If you used a spec-an, you could read what is a harmonic and what isn't. That might help the confidence aspect.

-Chris

#### jan.didden

Paid Member
Hi Jan,
That's the point. Measurement uncertainty.
If you used a spec-an, you could read what is a harmonic and what isn't. That might help the confidence aspect.

-Chris

The numbers are spectral components, no noise.
I should check the analyzer manual to see how they calculate with this stuff to get THD from the separate components.

Jan

#### DF96

Unless you know the phase of each component you have to do an RMS calculation as a best guess. Only if you know that the sig gen and circuit generate a given harmonic at the same phase can you do a straight arithmetic difference.

#### Charles Darwin

Couldn't you just convert into percentages and add those for a total?

Doing just that with your given numbers (-110dB + -105dB) gives me a total of 0.0008785% or -101.1251dB.
No idea if that is anywhere near reality though. Someone else would have to disprove or confirm.

Not sure if the limited number of decimal points of the online calculator I used is sufficiently accurate though.

Last edited:

#### jan.didden

Paid Member
Couldn't you just convert into percentages and add those for a total?

Doing just that with your given numbers (-110dB + -105dB) gives me a total of 0.0008785% or -101.1251dB.
No idea if that is anywhere near reality though. Someone else would have to disprove or confirm.

Not sure if the limited number of decimal points of the online calculator I used is sufficiently accurate though.

Hmmm. Interesting approach, although it would be a bit different for my numbers because -105 is the result of a generator at -110 and ´X´ resulting in finally -105. So in your approach X would be -110 - -105. I think.

Jan

#### Charles Darwin

If I treat the numbers as dBV, convert to Vrms, compute the difference and then back to dB I get -106.5dB with a generator that has -110dBV and a result of -105dBV. Not sure that's correct though.

Jan

That can't be right though, can it?

Surely the total distortion of the chain must be slightly higher than that of the device with the highest distortion in the chain.
Otherwise THD would subtract by running a signal through multiple devices.

#### jan.didden

Paid Member
Unless you know the phase of each component you have to do an RMS calculation as a best guess. Only if you know that the sig gen and circuit generate a given harmonic at the same phase can you do a straight arithmetic difference.

Yeah I guess so. Hmmm. So it would be something like a complex addition or subtraction. probably for each separate harmonic.

Jan

#### SY

Presumably, the harmonics of a signal are correlated, so add as voltage, not power.

#### Charles Darwin

Hmmm. Interesting approach, although it would be a bit different for my numbers because -105 is the result of a generator at -110 and ´X´ resulting in finally -105. So in your approach X would be -110 - -105. I think.

Jan

Sorry, missed that bit. I assumed wrongly that you were running a signal through two devices with known THD levels and wanted to predict the result.

#### jan.didden

Paid Member
Maybe I should say, the difference between gen and result is 4dB so the circuit makes the THD 4dB worse. So if the gen is -110 which is say 0.0003% then the circuit is about 1.6 times (4dB) as bad, or 0.0005%. Would that make sense?

Jan

#### anatech

Paid Member
Hi Jan,
I was more trying to have you see how much noise compared to signal there would be. This might determine how you add the numbers up. Yes, phase is not considered by looking at the result on the spec-an, but the real time addition or subtraction might show as you looked at each harmonic. A selective voltmeter might be handy right about now. (eg: HP 3581 type). A steady reading would tell you the sources are correlated.

-Chris

#### anatech

Paid Member
Hi Jan,
Those are excellent numbers you're throwing around there. It's always a pain when the DUT is close to the floor of your gear. With readings that low, have you tried turning off any lights in the area? Other noise like that can add another 10 dB to your numbers very easily.

-Chris

Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.